In triangle ABD, AC = CD = CB. Let AB = u and BC = v. Prove that DAB is a right angle triangle.

Question

AC is the midpoint of the assumed "right angle triangle" and is equidistant from the three vertices. Angle DAB is presumed to be 90.

Pls help me with this proof

Answer 1

Clarification AC is the midpoint of the HYPOTENUSE DB of the right angle triangle

Answer 2

since CD = CB, vector CD = v
If we let AD be vector z, then

u.z = (x-v).(x+v) = x.x-v.v
Since |x| = |v|, that is zero.

So, u and z are perpendicular.